Related papers: On the Construction of Even Order Magic Squares
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…
A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques, called strategies. In this paper, we consider the problem of generating such Sudoku instances.…
Equifacetal simplices, all of whose codimension one faces are congruent to one another, are studied. It is shown that the isometry group of such a simplex acts transitively on its set of vertices, and, as an application, equifacetal…
The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their…
This work presents arbitrary high order well balanced finite volume schemes for the Euler equations with a prescribed gravitational field. It is assumed that the desired equilibrium solution is known, and we construct a scheme which is…
The paper presents a simple, linear time, in-place algorithm for performing a 2-way in-shuffle which can be used with little modification for certain other k-way shuffles.
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…
Experiences with the implementation of strong Gr\"obner bases respectively standard bases for polynomial rings over principal ideal rings are explained: different strategies for creating the pair set, methods to avoid coefficient growth and…
We produce implicit equations for general biquadratic (order 2x2) B\'ezier triangle and quadrilateral surface patches and provide function evaluation code, using modern computing resources to exploit old algebraic construction techniques.
Many applications require multi-dimensional numerical integration, often in the form of a cubature formula. These cubature formulas are desired to be positive and exact for certain finite-dimensional function spaces (and weight functions).…
We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity is…
Matrix code allows one to discover algorithms and to render them in code that is both compilable and is correct by construction. In this way the difficulty of verifying existing code is avoided. The method is especially important for…
The shiftable Heffter arrays are naturally generalized to the shiftable Heffter spaces. We present a recursive construction which starting from a single shiftable Heffter space leads to infinitely many other shiftable Heffter spaces of the…
This paper is about producing a new kind of the pairs which we call it MS-pairs. To produce these pairs, we use an algorithm for dividing a natural number $x$ by two for two arbitrary numbers and consider their related graphs. We present…
We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-$k$ mosaic from incrementally constructed lower-order mosaics…
We construct a new compact semi-explicit three-level in time fourth-order finite-difference scheme for numerical solving the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are…